Use the discriminant to classify the graph. $100 x ^ { 2 } - 100 x y + 25 y ^ { 2 } + 12 y = 0$
A)The graph is a hyperbola.
B)The graph is a ellipse.
C)The graph is a circle.
D)The graph is a line.
E)The graph is a parabola.

Question

Use the discriminant to classify the graph.​ $100 x ^ { 2 } - 100 x y + 25 y ^ { 2 } + 12 y = 0$ ​
A)The graph is a hyperbola.
B)The graph is a ellipse.
C)The graph is a circle.
D)The graph is a line.
E)The graph is a parabola.

Quizplus · Accepted Answer

The discriminant of a quadratic function determines the number and type of solutions the function has. Since this graph is a parabola, it must be a quadratic function. The discriminant of such a function is Δ = b^2 - 4ac, where the coefficients a, b, and c come from the standard form of a quadratic function: f(x) = ax^2 + bx + c. In this case, the discriminant is negative, which means the function has two complex roots and the graph opens either upwards or downwards, but not horizontally or vertically. Therefore, the best choice is E, the graph is a parabola.

Use the Discriminant to Classify the Graph 100x2−100xy+25y2+12y=0100 x ^ { 2 } - 100 x y + 25 y ^ { 2 } + 12 y = 0100x2−100xy+25y2+12y=0

Use the Discriminant to Classify the Graph $100 x ^ { 2 } - 100 x y + 25 y ^ { 2 } + 12 y = 0$